Oops that was sort of a joke.
Myself and just about all of the folks I talk to here are electricians. As for the cord catching on fire, I hate it when the wire ends up being the fusable link in a circut.
All kidding aside even a skinny #14, 100' cord will not drop enough voltage to make much of a difference in how many amps the welder will pull. I plug mine into a 15 amp plug strip with the rest of the stuff on my bench. I did pop the breaker once when I filed the tip on the upper tong to get a bigger weld spot, the little spots work just as well they just don't look as good. The higher watt dimmers aren't cheap but one of 2400 watts or higher on the line side of the welder should let you control the one of these little spot welders. For as short as the heat cycle is on these welders you might even get by with a 1800 watt dimmer. check Lutrons web site.
While it is possable to fry a cord, if your wireing is ok and you don't have any pennys in your fuse box, the breaker should trip long before the fire starts. Well at least thats the theory anyways.